3. Using the estimated regression equation for estimation and prediction

Market model is a term used in finance to describe a linear regression model in which the dependent variable is the return on a stock and the independent variable is the return on the overall market. The market model is sometimes extended to include other independent variablesfor example, the return on a specific industry sector.

Company A is one of the leading software companies in the world. Suppose an analyst in an investment bank is creating a market model to predict returns on Company A stock from both market and industry returns. The multiple regression model is:

y

= =

0 + 1x1 + 2x2 +

where ywhere y	=	daily returns for Company A stockdaily returns for Company A stock
x1		daily returns for the Dow Jones Industrial Averagedaily returns for the Dow Jones Industrial Average
x2		daily returns for the NASDAQ Computer Index

Returns for the Dow Jones Industrial Average (DJIA) will indicate market returns, while those for the NASDAQ Computer Index (NCI) will indicate industry returns.

The analyst estimates the parameters , , and using daily returns for the period January 3, 2005, through December 30, 2005. The estimated multiple regression equation is:

y

=

0.0008 + 0.6404x1 + 0.6869x2

The coefficient 0.0008 in the estimated multiple regression equation is:

a. The estimated increase in average Company A stock return when the DJIA and NCI returns change by one unit

b. The estimated average Company A stock return when the DJIA and NCI returns are zero

c. The estimated change in average Company A stock return for a one-unit change in NCI return, keeping the DJIA return constant

d. The estimated change in average Company A stock return for a one-unit change in DJIA return, keeping the NCI return constant

Based on his study, the analyst expects an upturn for the overall market but a downturn for the computer industry. He expects a 2% = 0.02 return for the DJIA and a 1% = 0.01 return for the NCI.

When the DJIA return is 2% and the NCI return is 1%, the average Company A stock return for all trading days is estimated to be ____ (-0.61%, -1.95%, 1.96%, 0.67%), and the predicted Company A stock return for one specific trading day is _____ (-0.61%, 1.96%, -1.95%, 0.67%). This predicted return has _____ (a smaller value than, the same value as, a greater value that) the average return.

Using computer software, the analyst generates 95% confidence intervals and 95% prediction intervals for different return values of the DJIA and the NCI. The intervals are shown in the following table:

Table of 95% Confidence Intervals and Prediction Intervals
		Confidence Interval		Prediction Interval
x	x	Lower Limit	Upper Limit	Lower Limit	Upper Limit
2%	2%	4.94%	0.21%	14.37%	9.22%
2%	1%	4.69%	0.91%	13.78%	10.00%
2%	1%	5.35%	4.32%	13.04%	12.01%
2%	2%	5.88%	6.23%	12.88%	13.22%
1%	2%	3.80%	0.07%	13.64%	9.77%
1%	1%	2.59%	0.09%	12.88%	10.39%
1%	1%	2.96%	3.21%	11.84%	12.09%
1%	2%	3.54%	5.16%	11.53%	13.16%
1%	2%	5.04%	3.73%	13.02%	11.71%
1%	1%	3.09%	3.15%	11.94%	12.00%
1%	1%	0.06%	2.75%	10.23%	13.04%
1%	2%	0.26%	3.93%	9.61%	13.80%
2%	2%	6.11%	6.08%	13.08%	13.05%
2%	1%	4.20%	5.54%	11.87%	13.22%
2%	1%	0.77%	4.87%	9.85%	13.94%
2%	2%	0.36%	5.11%	9.06%	14.53%

When the DJIA return is 2% and the NCI return is 1%, the 95% confidence interval for the average Company A stock return is _____ (-3.09%, -4.69%, -2.59%, -4.20%) to ______ (0.09%, 5.54%, 3.15%, 0.91%) . The 95% prediction interval for the predicted Company A stock return is _____ (-12.88%, -11.94%, -13.78%, -11.87%) to _____ (10.39%, 12.00%, 10.00%, 13.22%) .

The interval for the average Company A stock return is _____ (wider, narrower) than that for the predicted Company A stock return, because you can estimate the average return for all trading days with _____ (less, more ) precision than you can predict the return for one specific trading day.

An investor has a portfolio consisting of 1,000 shares of Company A stock, which is priced at $40 per share. Assuming that the DJIA return is 2% and the NCI return is 1%, the 95% prediction interval for the predicted value of the investors portfolio is ______ ($44,748, $4,181, $35,252, $34,848) to ______ ($45,288, $44,156, $5,923, $34,712) . (Hint: If the Company A stock return is 5%, the value of one share will change from $40 to $40(105%) = $42. If the Company A stock return is 5%, the value of one share will change from $40 to $40(95%) = $38.)